Least squares channel identification for OFDM Systems

ABSTRACT

An OFDM system generates a channel estimate in the time domain for use in either a frequency domain equalizer or in a time domain equalizer. Preferably channel estimation is accomplished in the time domain using a locally generated reference signal. The channel estimator generates an initial estimate from a cross correlation between the time domain reference signal and an input signal input to the receiver and generates at least one successive channel estimate. Preferably the successive channel estimate is determined by vector addition (or subtraction) to the initial channel estimate. The at least one successive channel estimate reduces the minimum mean square error of the estimate with respect to a received signal.

This application is a continuation of U.S. application Ser. No.12/365,805, filed Feb. 4, 2009, entitled, “Least Squares ChannelIdentification for OFDM Systems,” which is incorporated by reference inits entirety.

BACKGROUND

1. Field of the Invention

The present invention relates to communication systems and, moreparticularly, to channel estimation in communication systems such asorthogonal frequency domain multiplexing or other systems that rely onchannel estimation.

2. Description of the Related Art

Orthogonal frequency domain multiplexing (OFDM) is a common modulationstrategy for a variety of commercially significant systems, includingfor digital subscriber line (DSL) communication systems and a number ofimplementations of the various IEEE 802.xx standards for wirelesscommunication systems. Often, an OFDM receiver will perform one or morefunctions that require channel estimation to allow the receiver toacquire a signal and to improve signal quality before the receiverbegins extracting bits.

OFDM receivers generally need to obtain signal timing information from areceived signal to help identify the start of a symbol within thereceived signal. A symbol is a predetermined number N_(b) of bitsuniquely mapped into a waveform over a predetermined, finite interval orduration. Each possible collection of bits is mapped to a unique signalaccording to the mapping or modulation strategy dictated by the OFDMscheme. Once an OFDM receiver determines when a symbol begins within thereceived signal, the receiver performs additional processing to improvethe quality of the received signal. In the processing to improve signalquality, the receiver attempts to achieve a target bit error rate (BER),often by implementing a linear filter, or equalizer, to condition theinput signal. The received signal can be significantly distorted bychannel imperfections. Ideally, the equalizer corrects the distortionsintroduced by the channel completely so that the receiver can demodulatethe signal with performance limited only by the noise level.

OFDM, unlike most other modulation strategies commonly used incommunication systems, can include two equalizers to improve signalquality: a time equalizer (TEQ) and a frequency equalizer (FEQ). SomeOFDM applications such as DSL include a time equalizer while others,such as systems that implement current wireless standards, do not demanda time equalizer. All practical OFDM receivers have a frequencyequalizer. Whether a receiver includes a time equalizer or only afrequency equalizer, the receiver needs to perform channel estimation toat least initially determine values of the equalizer coefficients beforethe equalizer can be used to improve the signal quality. Determining thecoefficients for frequency equalizers is typically performed in thefrequency domain.

Conventional OFDM receiver circuitry down converts the received signalto baseband and then analog-to-digital converts that signal to producethe information signal s(n) that is input into the OFDM processingcircuitry shown in FIG. 11. The signal s(n) is input 1101 to a firstprocessing element 1110 that removes the cycle prefix (CP) from thesignal s(n). A conventional OFDM transmitter adds a CP of length N_(CP),which consists of the last N_(CP) samples, to a unique signal waveformof length N so that the digital signal that the transmitter converts toanalog is of length N+N_(CP). The initial step of the receiver's reverseconversion process then is to remove and discard the added cycle prefixN_(CP) samples. Following that step, a serial to parallel conversionelement 1120 organizes and converts the serial signal into parallel forfurther processing. The cycle prefix can be removed either before orafter the serial to parallel conversion.

The parallel data output from the element 1120 is provided to a fastFourier transform (FFT) processor 1130 that converts the time domainsamples s(n) to a set of frequency domain samples R_(i)(k) forprocessing. The received OFDM signals are assumed to be corrupted by thechannel, which is assumed for OFDM to introduce amplitude and phasedistortion to the samples from each of the frequencies used in the OFDMsystem. The FEQ 1150 applies an amplitude and phase correction specificto each of the frequencies used in the OFDM system to the varioussamples transmitted on the different frequencies. To determine thecorrection to be applied by the FEQ 1150, the FEQ 1150 needs an estimateof the channel's amplitude and phase variations from ideal at eachfrequency. In FIG. 11, the frequency domain channel estimate 1140element determines the channel estimate that is used by the FEQ 1150.

A conventional OFDM channel estimator 1140 used in FIG. 11 typicallyuses a pilot tone sequence or other signal that has predictablecharacteristics such as known bits and carrier locations. The pilottones are generally dictated by the relevant standards. The frequencyequalizer 1150 receives the signals from the fast Fourier transformprocessor 1130 and the channel estimates from the estimator 1140 andequalizes the signal. The output of the equalizer 1150 is provided to aparallel to serial element 1160 that converts the parallel outputs ofthe equalizer to a serial signal that is then provided to thedemodulator 1170. The structure and function of the demodulator variesand generally corresponds to a standard or particular OFDM communicationscheme.

In many applications, there is a requirement to model an unknown systemor process with a transfer function. The transfer function takes theform of either an infinite impulse response (IIR) or a finite impulseresponse (FIR) polynomial or filter. The former is also referred to asan auto-regressive moving average (ARMA) model and the latter simply asa moving average (MA) model.

The process of system identification or, equivalently, characterization,can typically be described as shown in FIG. 1. The input 101 to theunknown system 110 and the output 112 are used by the identificationprocess to determine the ARMA or MA models. Modern identificationmethods are digitally implemented, so the signals s 101 and y 112 areassumed to be sampled, without a loss of generality on the methods'applicability and performance. From linear system theory, therelationship between the input and output signals is simply defined as aconvolution, that is,

$\begin{matrix}{{y\lbrack n\rbrack} = {\sum\limits_{l = {- \infty}}^{+ \infty}\;{{h\lbrack l\rbrack}{{s\left\lbrack {n - l} \right\rbrack}.}}}} & (1)\end{matrix}$Therefore, if the samples of the input signal s 101 are known and theunknown system's output signal y 112 samples are measured, the linearestimation of the unknown system can be achieved though variousstrategies.

The signals s 101 and y 102 are better described in a sampled system byadding the sampling index n which maps the value of each signal sampleto an interval of time. The modeled unknown system response h[l] has thesame sampling interval as the signals s[n] and y[n]. The discussionshere assume that input and output signals are sampled at the samesampling interval. Variations on these assumptions do not affectperformance of presently preferred implementations of the presentinvention.

The simplest strategy to identify an unknown system is to use an inputsignal for system identification that is s[0]=1, s[n]=0 for values ofn≠0, and ranging between −∞ and +∞. This impulse response is termed aDirac delta function and it has the desired effect in equation (1) ofy[n]=h[n]. However, in most practical systems, using a Dirac deltafunction for system identification is not possible due to the practicaldifficulty in generating such an input signal, combined with hinderingoperational conditions such as the typical throughput rates incommunication systems.

Since the right side of equation (1) is a dot-product definition, theoutput 112 is observed over N samples and the MA time span of h[l] isassumed to not be significant beyond L samples, then a matrixformulation of equation (1) is readily obtained:y=Hs=Sh  (2)where the N-by-L matrix H(S) has rows with the time-shifted samples, asa function of n, and the vector L-by-1 s(h) is fixed over the time spanin y. That is, the entries in the vector y arey[m]=[y[n]y[n+1] . . . y[n+N+1]]^(T)  (3).The time index m is used to denote the possibility that the time-seriesof the vector y may not have a one-to-one correspondence with the inputsamples y. On the other hand, the index m in an OFDM system does have aone-to-one correspondence with the received OFDM symbol, defined as thetime interval containing N=FFT length+cycle prefix samples. For example,in the WiMAX standard, this value can be N=1024+128=1152 samples.

Linear algebra notation is used to describe the operations due to itssuccinct representation and due to its immediate parallel to a hardwaremultiply-and-accumulate operation that performs a dot-product betweentwo vectors, or the multiplication of a matrix row and a vector, as inequation (2). Those skilled in the art generally also exploit symmetricproperties in the matrix to reduce complexity in this matrix-vectormultiplication.

SUMMARY OF THE PREFERRED EMBODIMENTS

An aspect of the present invention provides a receiver, comprising areference signal generator that generates a time domain reference signalresponsive to a received frequency domain pilot signal. The receiverincludes a channel estimator responsive to the time domain referencesignal and generating a time domain channel estimate.

Another aspect of the present invention provides a receiver, comprisinga reference signal generator that generates a local reference signalresponsive to a received frequency domain pilot signal extracted from aninput signal. The receiver includes a channel estimator responsive tothe local reference signal and the input signal. The channel estimatorgenerates an initial channel estimate from a cross-correlation based onthe local reference signal and the input signal. A correction modulegenerates a channel correction to the initial channel estimate. Thecorrection module is responsive to the initial channel estimate togenerate a set of basis filters and to generate the channel correctionas a combination of the set of basis filters and a set of coordinatesdefined in the set of basis filters. A channel module adds the initialchannel estimate with the channel correction and generates a furtherchannel estimate.

Still another aspect of the present invention provides a frequencydomain receiver for a communications system, the receiver comprising areference signal generator that generates a time domain local referencesignal. A channel estimator responsive to the local reference signal andthe input signal generates a time domain initial channel estimate from across-correlation based on the local reference signal and an inputsignal. A correction module generates a channel correction to theinitial channel estimate. The correction module responsive to theinitial channel estimate to generate a set of basis vectors and togenerate the channel correction as a combination of the set of basisvectors and a set of coordinates defined in the set of basis vectors. Achannel module that adds the initial channel estimate with the channelcorrection and generates a time domain further channel estimate, whereinthe further channel estimate is a minimum error channel estimate in aleast squares sense. A filter module that generates a signal filterbased on the further channel estimate and filters the input signal.

BRIEF DESCRIPTION OF THE DRAWINGS

Aspects of the present invention are illustrated in the attacheddrawings and can be better understood by reference to those drawings inconjunction with the detailed description. The attached drawings form apart of the disclosure.

FIG. 1 schematically illustrates the general problem of determiningchannel characteristics based on information known about the signalbefore it is transmitted through the channel and information measuredabout the signal after it has passed through the channel.

FIG. 2 schematically illustrates a SISO receiver according to apreferred embodiment of the present invention.

FIG. 3 schematically illustrates a MIMO receiver that implements smartantenna combining according to a preferred embodiment of the presentinvention.

FIG. 4 schematically illustrates a MIMO receiver that implements MIMOcombining according to a preferred embodiment of the present invention.

FIG. 5 schematically illustrates the structure of a conventional WiMAXframe.

FIG. 6 schematically illustrates the structure of one example of areference signal frame that is locally generated based on receivedinformation and specifically a frame structure that can be used forreceiving a WiMAX communication.

FIG. 7 schematically illustrates aspects of a deterministic least squarechannel estimation circuit according to preferred aspects of the presentinvention.

FIG. 8 schematically illustrates aspects of a stochastic least squarechannel estimation circuit according to preferred aspects of the presentinvention.

FIG. 9 graphically presents signal reception using a base linecross-correlation channel estimate as compared with a channel estimationperformed according to the circuitry illustrated in either FIG. 7 orFIG. 8.

FIG. 10 graphically presents the packet error rates achieved using abase line cross-correlation channel estimation strategy as compared witha channel estimation performed according to the circuitry illustrated ineither FIG. 7 or FIG. 8.

FIG. 11 schematically illustrates a conventional orthogonal frequencydomain multiplexing (OFDM) receiver configuration.

FIG. 12 schematically illustrates an OFDM receiver in accordance withaspects of the invention that provides interference mitigation in anillustrative two base station environment.

FIG. 13 graphically illustrates packet error rates observed insimulations of the performance of an implementation of the FIG. 12 OFDMreceiver under different levels of interference.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

A preferred aspect of the present invention provides a channel estimatefor use in either a frequency domain equalizer or in a time domainequalizer. Preferably channel estimation is accomplished by generatingan initial channel estimate. For example, a channel estimator maygenerate an initial channel estimate from a cross correlation between alocally generated reference signal and a received signal input to thereceiver. Preferably the channel estimator generates at least onesuccessive channel estimate by determining a correction to the initialchannel estimate where the correction is made by vector addition to theinitial channel estimate. The at least one successive channel estimatepreferably reduces the minimum mean square error of the estimate withrespect to a received signal.

In particularly preferred implementations, the successive channelestimate is determined by generating a set of basis vectors, separatelygenerating a set of coordinates with reference to that set of basisvectors, combining the set of basis vectors and the set of coordinatesto generate a channel correction vector and adding the channelcorrection vector to the initial channel estimate to generate thesuccessive channel estimate.

Another aspect of the present invention provides a communication systemthat generates a channel estimate in the time domain. Preferredimplementations of this aspect estimate one or more channels in the timedomain using a locally generated reference signal. The channel estimatorgenerates an initial estimate from a cross correlation between the timedomain reference signal and an input signal input to the receiver andgenerates at least one successive channel estimate. Preferably, at leastone successive channel estimate reduces the minimum mean square error ofthe estimate with respect to a received signal. This time domain channelestimation strategy is implemented advantageously with respect tovarious communication systems including, for example, OFDM systems suchas WiMAX systems.

The fundamental problem of channel estimation for a communication systemis shown FIG. 1, where the channel is represented as an unknown lineartransfer function and is to be identified by its impulse response.Typically, though not exclusively, a linear system is assumed to have afinite impulse response (FIR), or moving average model, which is asuitable assumption for many practical communication applications. Inthis example, the impulse response h[l] is to be determined solelythrough observations of the input s 101 and output y 112 signals. Theestimate of h[l] 110, noted as g[l] 122, is determined from the twoobserved signals s 101 and y 112.

Using statistical signal analysis, the relationship between the sampledinput s[n] and the sampled output y[n] from a given filter h[l] is

$\begin{matrix}{{{r_{sy}\lbrack d\rbrack} = {\sum\limits_{l = {- \infty}}^{+ \infty}{{h^{*}\lbrack l\rbrack}{r_{s}\left\lbrack {d - l} \right\rbrack}}}},} & (4)\end{matrix}$where, for the signals typical of communication systems,r _(s) [d]=E{s*[d]s[n+d]}r _(sy) [d]=E{s[d]y*[n+d]}  (5).Equation (5) indicates that the unknown system's impulse response can beobtained from the cross-correlation r_(sy)[d] between the input signals[n] and the output signal y[n]. If r_(s)[d] is ideally a “spike”consisting of a 1 at the delay d=0 and zero for d≠0, r_(s)[0]=1 and zerootherwise (that is, an ideal Dirac delta function), thecross-correlation between the unknown system output y[n] and the inputs[n] reveals the impulse response h[l] for the values of n=d. Defineg[l] as follows,

$\begin{matrix}{{g\lbrack l\rbrack} = {{r_{sy}\lbrack l\rbrack} = {\sum\limits_{i = {- \infty}}^{+ \infty}{{h\lbrack i\rbrack}{r_{s}\left\lbrack {l - i} \right\rbrack}}}}} & (6)\end{matrix}$as the output of the modeling module 120 used to approximate h[l].Preferred aspects of the present invention can be used to provide a bestconstrained estimate of h[l] given g[l], regardless of how r_(s)[d]differs from a Dirac delta function.

Equation (4) illustrates an approach to identify the unknown system's110 impulse response. Under most practical circumstances, theauto-correlation r_(s)[d] does not have the ideal Dirac delta functionproperty of being one at a delay of zero and zero otherwise. In fact,the auto-correlation may be unknown a priori or the auto correlation maychange with time. As a result, the determined cross-correlation g[l] isnot the unknown system's impulse response, but instead g[l] is distortedby the non-ideal auto-correlation r_(s)[d] from the input signal as itis convolved with the system's impulse response.

The accuracy demanded in the unknown system's impulse responseestimation is a function of the process that follows to alter the signaly 112. The process may be as simple as a filter f[k]. Although thefilter f[k] can take on many forms, depending on the application, incommunication systems the filter f[k] is used to “clean up” thecommunication channel output y[n] 112 to obtain a “best” estimate of thechannel input s[n] 101. An example of a preferred implementationenvironment, which is useful for illustrating aspects of the presentinvention, is determining the equalizers f[k] for an OFDM communicationsystem. Modern communication systems employing OFDM to achieve high bitrates estimate the channel for each OFDM symbol interval. The channelestimate should be robust and sufficiently accurate, but also should besufficiently computationally simple to allow the channel to be estimatedin a small interval of time.

Preferred embodiments of the present invention can be used to providetime-domain channel estimation through sub-space computations of thetransmit signal's 101 statistics. A particularly advantageous strategyfor time-domain channel estimation is identified here as least squareschannel estimation (LS-CE).

LS-CE can provide an impulse response estimate g[l] 122 that minimizesthe error in h[l] 110 due to r_(sy)[d] (in equation (4)) in the leastsquares sense, by removing at least some of the undesired imperfectionsin r_(s)[d] due to its deviation from the Dirac delta function.Generally speaking, this LS-CE approximation of the impulse responseestimates a correction to be applied to r_(ys)[d],g[l]=r _(ys) [l]−G(l,{circumflex over (r)} _(sy) [l],{circumflex over(r)} _(s) [l])  (7),for 1=0, 1, 2 . . . , L−1. That is, a linear function G(·) of thecross-correlation and auto-correlation estimates is used to subtract theimperfections introduced by r_(s)[d]. This approach is stable and ofgreatly reduced complexity as compared to a de-convolution of r_(ys)[k].Statistics related to the unknown system are not required. Furtherfeatures of the formulation in equation (4) include the limited“support” needed for the values of l in the time span of interest.

Determining the linear function G(·) uses a formulation, in linearalgebra terms, that generates a subspace basis from a vector consistingof the values in r_(ys)[l], followed by a decomposition of theauto-covariance matrix with entries from {circumflex over (r)}_(s)[l].Therefore, for L significant coefficients in h[l], the estimate g[l] isg=r _(sy) −Gb  (8)where {g, r_(ys)} are L-by-1 vectors and G is a L-by-D matrix of columnsgenerated from the vector, but not including r_(ys). The D-by-1 vector bis derived from the auto-covariance matrix Rss, whose entries are givenby the transmit signal's auto-correlation function and G preferably isdetermined through a least-squares formulation. D is termed theapproximation index, as is explained below.

Any practical OFDM communication system must be capable of operating ina mobile environment. As such, the equalization process of the receivedsignal should be capable of removing time varying channel distortionsand should provide a channel estimate for each received OFDM symbol. Thewireless communication standards aid in this channel estimation. In thisparticular system identification application, the channel constitutesthe unknown system 110, and corrections to the received signal must beeffected by a filter applied to the unknown system output 112. Anothercommon aspect of currently available mobile or fixed location OFDMmodems is the number of antennas and transmission schemes used toexploit the number of antennas at the transmitter and receiver. Theadded antennas increase the system's sensitivity to channel estimationerrors and increase the necessary estimation accuracy.

The simplest transmission scheme is one with a single transmit andreceive antenna, as shown in FIG. 2. This configuration is termedsingle-input single-output (SISO) 240, which is the classicconfiguration for a communication system, whether wired or wireless,mobile or fixed. The salient feature for this configuration, as comparedto other antenna schemes, is the single channel 210 that results in thesimplest receiver. In this configuration, the receiver must identify thechannel 210, using the least square channel-estimator 220, and then afilter 230 is calculated based on the channel estimate 222 to equalizethe channel and replicate the transmitted signal 201 at the filteroutput 232. This operation is repeated for each symbol, whose samplesare delineated in the input signal s[n] 201 with an additionaltime-synchronization circuit. This conditioning by the SISO receiver 240is shown to operate on a time domain signal, which in OFDM correspondsto the application of a time equalizer (TEQ), and more generally canhave other components including a frequency equalizer (FEQ).

The equalizer f[n] in an OFDM communication system is calculated foreach symbol to establish a high-throughput link. The equalizer's abilityto remove distortions depends on the channel estimation accuracy and theeffective noise floor in the measurements. Obtaining an accurateestimate of the channel's reflective path delays and amplitudevariations is important to achieving higher throughput rates. Higherthroughput rates in OFDM are achieved in part by modulating the bitsaccording to modulation schemes that are highly sensitive to channeldistortions and noise. Such sensitive modulation schemes especiallybenefit from an equalizer that is more precise in its ability to removechannel distortions. From another perspective, use of a sensitivemodulation scheme places a minimum requirement for accuracy in channelestimation.

Applying equation (6) to an OFDM system can be ineffective because ofthe auto-correlation properties of the transmitted symbol. The values ofr_(s)[d] in equation (5) for d≠0 are not sufficiently suppressed toallow sensitive modulation schemes, which could allow a higherthroughput, to be implemented. In severe channels, it is possible thatno successful link will be established between two terminals if thechannel estimate is done with equation (6) without further corrections.

OFDM offers, under certain assumptions about channel characteristics,the ability to calculate and apply the filter in the frequency domain,which does not require the formulation in equation (4) to estimate thechannel. This particular equalizer is termed the frequency equalizer(FEQ), and it is always required in an OFDM receiver, though itsefficiency is compromised when the channel assumptions are violated.

Under practical conditions, OFDM systems may advantageously incorporatea time-domain channel estimate, even when the OFDM receiver incorporatesonly an FEQ. The number of parameters to estimate in the time domainchannel estimation is smaller compared to the number of coefficients todetermine for the FEQ. For example, in the WiMAX standard, the channelis assumed to not exceed 128 coefficients, but the OFDM symbol has 840active carriers so that the number of parameters to estimate is reducedby a factor of seven in the time domain. Furthermore, estimation in thetime domain is not affected by the loss of orthogonality that can occurthrough the fast Fourier transfer (FFT) transformation due toimperfections in the channels (e.g., carrier offset) that causeinter-carrier interference (ICI). Therefore, these properties oftime-domain channel impulse response (CIR) estimation provide a robustbasis for estimating the channel.

FIG. 3 shows another configuration of interest, where there is a singletransmission stream 301 received with two antennas. Consequently, thereare two channels to equalize and to combine to obtain an improvedestimate of the singly transmitted signal 301. In this configuration, itmay be advantageous to utilize equalizers 330 for each received signal311 and 312, and then apply smart antenna 350 type combining todesirably process the diversity received signal. See, for example,Godara, Smart Antennas (2004). At its best performance, smart antennacombining can offer a 3 dB power gain versus a single antennaconfiguration. In the case of OFDM, the time domain filters 330 may beoptional. In an OFDM receiver the smart antenna 350 combining may beapplied in the frequency domain, as those skilled in the art candetermine the time versus frequency domain implementation.

The filter 330 and smart antenna 350 conditioning on the input signalsachieve their best performance as a function of the channel estimationaccuracy. The present invention offers high accuracy at low complexityby estimating the channel in the LS-CE module 320, which processes eachinput signal available (e.g., 311 and 312) to output channel estimates322 for equalization, and additional cross terms 324 for improved smartantenna combining 350 and greater fidelity in the estimate 351 of theinput signal 301. The reference signals 341 are devised in accordancewith the LS-CE processing requirements, derived from existing referencesignals embedded in OFDM symbols as specified in standards, for example.

The other alternative multiple-antenna configuration possible in an OFDMreceiver is the MIMO receiver 440 in FIG. 4. In this configuration, thetransmitter simultaneously transmits a plurality of signals, with twoshown in FIG. 4, each affected by different channels 410. Each signal(411 and 412) received from a respective one of a plurality of antennasat the receiver has a combination of each transmitted signal (401 and402). As is the case for a smart antenna receiver 340, the MIMO receiver440 may include a time-domain filter 430, and preferably processes theMIMO combining 450 and separating in the time domain. The filter andMIMO combining can also be performed in the frequency domain in the caseof OFDM signals.

Unlike the condition in the smart antenna receiver 340, the MIMOcombiner 450 extracts plural signals (451 and 452) sent simultaneouslyby the transmitter. This is the principal appeal of a MIMO system, whichincreases the throughput as compared to the same link coupled to a SISOreceiver 240.

The performance of filter 430 and MIMO 450 conditioning on the inputsignals is a function of the channel estimation accuracy. Receiversaccording to some aspects of the invention can be implemented so as tooffer such high accuracy at low complexity by estimating the channel inthe LS-CE module 420. Preferred implementations of the LS-CE module 420process each available input signal (e.g., 411 and 412) to outputchannel estimates 322 for equalization and additional cross terms 424for improved MIMO combining 450 and greater fidelity in the estimate 451of the input signals 401 and 402. The reference signals 441 preferablyare devised in accordance with the LS-CE processing requirements forMIMO receivers, derived from existing reference signals embedded in OFDMsymbols as specified in standards, for example.

To use an LS-CE to estimate the unknown channel(s), two input signalsare required, including a reference signal. In the case of OFDM signals,and in particular drawing from the WiMAX (IEEE 802.16) standard, thereference signal is derived from training signals embedded in thetransmitted symbols.

An OFDM symbol includes a number of samples related to the size of thefast Fourier transform (FFT) the OFDM modulator uses to generate thetime-waveform. The OFDM symbol also includes a pre-determined number ofsamples from the beginning of the symbol that are copied and appended tothe end of the symbol. These copied samples are termed the cycle prefix.The symbol rate is the inverse of the duration of the totality of theOFDM symbol and the cycle prefix samples. In the WiMAX system, symbolsare grouped in time to form a frame. This is demonstrated in FIG. 5.

Each OFDM symbol transmitted within a frame has a function and astructure according to the information it carries. The first symbolcontains no user information or data. The entire first symbol consistsof a predetermined number of carriers, each modulated with an a prioriknown value. This kind of symbol is often referred to as a pilot symbol510, because the symbol can be replicated perfectly at the receiver forcomparison. Additional symbols are then transmitted that containinformation for configuration of the network for all users in thenetwork. These symbols are often termed control symbols 540. Theremaining symbols are configured to simultaneously include theinformation or data (data modulated subchannels 520) transmitted to eachuser and the additional pilot subchannels 530.

An OFDM symbol's time domain samples derive from a plurality ofmodulated carrier signals in the frequency domain, which are thengrouped together into a singular time domain waveform through addition.This addition is effectively computed with an inverse fast Fouriertransform (FFT). Then, the standard provides a systematic assignment ofa subset of the active carriers, each carrier also termed a subchannel,to be modulated with a known set of carrier amplitude and phaserotations. These are the pilot subchannels. The standard may dictatethat these subchannels need not be contiguous. The information bits tobe transmitted to a user are likewise mapped into amplitude and phaserotations according to the specifications in the standard.

The user symbols containing the information bits can be sentsimultaneously with the training pilot subchannels (known a priori atthe receiver). If the channel conditions do not cause a loss of assumedproperties about the OFDM symbol, the received symbol will have nosignificant interference between the pilot and data subchannels.Therefore, the receiver can systematically extract the pilot subchannelsand compare the pilot symbols to their ideal state and use the observederrors to devise a frequency domain channel estimate.

Preferred embodiments of the present invention use the pilot subchannelsdifferently, in that the channel estimation preferably is accomplishedin the time domain. In the time domain, the OFDM symbol has a pluralityof data and pilot subchannels added together into a short-durationwaveform, and thus, the receiver does not have an a priori waveform thatcan be generated at the receiver for a local reference (e.g., 241, 341and 441). The separation of these data and pilot subchannels is readilyaccomplished in the frequency domain as is illustrated in FIG. 5. Thetime domain representation of the pilot symbol subchannels 510 can bereplicated ideally at the receiver since there are no data subchannelstransmitted for that symbol.

Aspects of the present invention preferably locally generate and use areference waveform generated to have the symbol structure of a desiredsignal. For example, the reference waveform may be generated to have theform of an OFDM frame, as shown in FIG. 6. For the embodiments describedhere it is particularly advantageous to provide a reference waveform inthe time domain. The time domain OFDM reference waveform incorporatesthe pilot symbol 610 (FIG. 6) which is a duplicate of the pilot symbol510 as shown in FIG. 5. The duration for the control symbols 540 may beignored by the LS-CE implementations in the case of WiMAX by generatingzeroed symbols 640 as shown in FIG. 6. The system preferably generates areference signal corresponding to the pilot and data symbols 530 and 520that are transmitted over the rest of the frame by replicating the pilotsubchannels 530 in locally generated reference frame 630, while“zeroing” the data subchannels 620. That is, the system generates thedata subchannel 620 to correspond to modulated data with all of the datavalues set to zero.

The minimum mean square error (MMSE) formulation for the time-domainchannel estimation (TDCE) in WiMAX uses a linear channel model, suchthat,y=Hx+n  (9),where x is the transmitted signal, n is the noise vector and y is thereceived signal vector. The matrix H is the channel convolution matrix.The MMSE estimation for the transmit signal x is given by,{circumflex over (x)}=R_(yx)R_(yy) ⁻¹y  (10),where R_(xy) is the cross-correlation between input and output variablesx and y. Note that the specific node at which the received signal y isidentified with respect to the receiver circuitry is somewhat arbitraryand can be selected so that it does not impact on the analysis discussedhere. Even when applied in the frequency domain, the formulation israther complex:Ĥ _(MMMSE) =R _(HH) _(p) (R _(HH) _(p) +σ_(n) ²(XX ^(H))⁻¹)⁻¹ Ĥ_(LS)  (11),where X is a diagonal matrix with the transmit signal's spectrum(FFT(x)),Ĥ_(LS)=X⁻¹Y  (12),and Y is a diagonal matrix with the spectrum for the received signalobtained, for example, from a fast Fourier transform (FFT) of thereceived signal. H_(p) is the channel frequency response (CFR) for thepilot subcarriers. Use of singular value decomposition can reduce thecomplexity of this operation.

A simple method to estimate channels is via the cross-correlation of alocally generated and conjugated reference signal with the signalreceived at the input of the receiver. This cross-correlation will findthe “copies” of the reference signal in the received signal at thedelays of the channel. On the other hand, the underlying condition forthis cross-correlation to work is that the auto-correlation property ofthe sequence is (practically) a single spike when aligned, and nearlyzero elsewhere. This is the case for most pseudonoise (PN) sequencesused in spread spectrum communications and generally sufficiently truefor CDMA cellular systems. In contrast, OFDM does not have such aproperty.

A particularly preferred approach for an OFDM system is tocross-correlate a conjugated locally-generated reference signal with thesignal received from the channel (which can be designated the input tothe receiver) and to use that cross-correlation result as an initialestimate of the channel. This approach then revises the channel estimatefrom this initial channel estimate over D steps. Starting with anoiseless case, the linear model from equation (12) states therelationship of the transmitted symbol and the channel and can beequivalently stated as,y=Hx=Sh  (13)where S is the matrix with the values of x as a convolution matrix. Thevector y is the received OFDM symbol.

A fundamental assumption for the least squares (LS) channel estimationstrategy is that starting with an initial estimate, such as h₁, thereceiver can make an estimate that converges toward the ideal channel h.The second assumption is that a step from D to D+1≦D_(stop) does notincrease the MMSE on the estimation error to the true channel, for someD_(stop)≦L, where L denotes the channel length. This assumption informsthe idea of repeated revisions on the original estimate and subsequentmodifications.

Based on these assumptions,y=Sh≅S(h ₁ +G _(D) b)  (14)where G_(D) is termed the D-step revision matrix, or the revision matrixat approximation index D. The initial guess (initial channel estimate)h₁ is preferably determined to minimize complexity. The revision matrixis of dimension L×D, and the coordinate vector b is D×1. Then, thefollowing equivalences to equation (14) are apparent,S ^(H) ŷ=S ^(H) S(h ₁ +G _(D) b)={circumflex over (R)} _(SS)(h ₁ +G _(D)b)  (15)G _(D) ^(H) S ^(H) ŷ=G _(D) ^(H) {circumflex over (R)} _(SS) h ₁ +G _(D)^(H) {circumflex over (R)} _(SS) G _(D) b  (16)and noting that y−ŷ=e_(D) is the error on the revision matrix G_(D),thenG _(D) ^(H) S ^(H) y+G _(D) ^(H) S ^(H) e _(D) =G _(D) ^(H) {circumflexover (R)} _(SS) h ₁ +G _(D) ^(H) {circumflex over (R)} _(SS) G _(D)b  (17).Choosing D for G_(D) ^(H)S^(H)e_(D) to be sufficiently small givesG _(D) ^(H) S ^(H) y=G _(D) ^(H) {circumflex over (R)} _(SS) h ₁ +G _(D)^(H) {circumflex over (R)} _(SS) G _(D) b  (18)where S^(H)y is a cross-correlation of the received signal with theconjugate of the reference signal. As discussed in greater detail below,the computational complexity can be further reduced by defining h₁ (theinitial guess) to be this cross-correlation.

Equation (15) has two unknown variables: the revision matrix G_(D) andthe coordinates for the revision matrix. A suitable approach to generatethe revision matrix G_(D) is to use an initial guess vector h₁ and theLanczos strategy, or the Arnoldi strategy if {circumflex over (R)}_(SS)is not Hermitian. Either strategy computes G_(D) given a seed vector h₁so that,G_(D) ^(H)h₁=0  (19).That is, G_(D) is determined to be orthogonal to the initial guessvector h₁ and preferably provides a basis that spans the space toproject the initial guess vector to the desired correction vector.Preferred implementations then continue to solve for the coordinatesthat provide the improved channel estimate h_(D) with h₁=S^(H)y as aninitial condition seed vector:−G _(D) ^(H) {circumflex over (R)} _(SS) h ₁ =G _(D) ^(H) {circumflexover (R)} _(SS) G _(D) b  (20)b=−(G _(D) ^(H) {circumflex over (R)} _(SS) G _(D))⁻¹ G _(D) ^(H){circumflex over (R)} _(SS) h ₁ =−T _(D) ⁻¹ G _(D) ^(H) {circumflex over(R)} _(SS) h ₁  (21)and then,h _(D) =h ₁ +G _(D) b  (22)is the channel estimate.

The Lanczos strategy, which is presently a particularly preferredstrategy to obtain G_(D), has a “self-stop” feature, in that it ceasesto generate orthogonal basis vectors (the columns of G_(D)) once aneigenvector is found. This is the designed or intended outcome for theLanczos and Arnoldi strategies.

If {circumflex over (R)}_(SS) is a diagonal matrix, then the strategiesstop with the cross-correlation estimate h₁. This is because any vectoris an eigenvector to an identity matrix. However, this is why h₁preferably is defined to be the cross-correlation vector h₁≡S^(H)y,which is the perfect channel estimate for an uncorrelated signal x(e.g., x is white Gaussian noise). Therefore, the only condition underwhich {circumflex over (R)}_(SS) is a scaled identity matrix is when thesignal x is white Gaussian noise or a pseudonoise sequence withzero-valued auto-correlation outside the zero-delay lag.

When {circumflex over (R)}_(SS) is an identity matrix, it commutes withany matrix and the following conditions hold:b=−T _(D) ⁻¹ G _(D) ^(H) {circumflex over (R)} _(SS) h ₁ =−T _(D) ⁻¹{circumflex over (R)} _(SS) G _(D) ^(H) h ₁ =−T _(D) ⁻¹ {circumflex over(R)} _(SS)0=0   (23).henceh _(D) =h ₁ +G _(D) b=h ₁  (24).Another observation relates to the “richness” of {circumflex over(R)}_(SS). If the transmitted signal has poor auto-correlationproperties, then the value of D that results in a target estimationerror power ξ=e_(D) ^(H)e_(D), will be lower than one with goodauto-correlation properties.

Preferred implementations of the present invention preferably implementan LS-CE in one of two ways, depending on the statistical properties ofthe OFDM signal characteristics for a given standard. One preferableimplementation is termed the “deterministic LS-CE” to denote that thelocally generated reference signal (e.g., 241, 341 or 441) is a locallygenerated signal with the construction illustrated in FIG. 6, in thecase of WiMAX. If the second-order statistics for the transmit signalare stable for the channel under consideration, then a “stochasticLS-CE” implementation like that illustrated in FIG. 8 may be preferred.

FIG. 7 shows a deterministic LS-CE of a type that can advantageously beimplemented in an OFDM receiver (e.g., 220, 320 or 420). The signals inFIG. 7 are noted as linear algebra constructions to provide a parallelto the equations that describe the LS-CE. Furthermore, the illustratedcircuits are made up of simple multiply-and-accumulate (MAC) hardwareelements that are readily adapted to linear algebra operations such asmatrix-vector or vector-vector multiplications. Those skilled in the artwill readily design appropriate hardware with low complexity for anyspecified operation shown in FIG. 7. Alternately, the FIG. 7 or othercircuitry in this description could be implemented within a digitalsignal processor or in a general purpose processor.

The locally generated reference signal from FIG. 6, constructed from onesymbol by the convolution matrix S 703, is multiplied by the receivedsignal vector y 701 (input to the receiver) to produce the initialchannel estimate h₁ 722. The initial channel estimate is simply theconvolution of the two signals represented in equations (1) and (2).Preferably these signals are constructed so that the receiver timing isestablished to align a symbol in the vector y 701 with the referencesymbol in S 703 so that the initial estimate vector h₁ 722 captures allthe replicas of the symbol in the channel significant to the receiverimplementation. The length L for the channel estimate, and consequentlythe dimension of h₁ 722 as an L×1 vector, preferably is determined bysimulation and expected conditions in the implementation environment.

The basis filter module 730 determines D basis filters, where D is afixed parameter determined based on performance goals and simulationverifications, preferably using the Lanczos method. Under most knowncircumstances, the value of D will be somewhere between three and five.Preferably, the matrix G 732 then consists of D columns corresponding tobasis filters determined through the Lanczos method.

The gain in the LS-CE is used to reduce the dimension of the receivedsignal's auto-covariance matrix. This reduction in dimension is achievedwith the matrix G 732. The dimension reduction module 740 performs thisdimensionality reduction by taking the correlation matrix with thereference signal S 703, which is N×L, and produces two matrix outputs:P_(S), a D×L matrix, and T_(SS), a D×D matrix. The hardware generatesthese outputs through the following definitions:P_(S)=G^(H)S^(H)S  (25)andT_(ss)=P_(S)G  (26).Preferably the order of multiplication in equation (25) is selected tominimize the number of MACs required. As discussed above, N is thelength of the vector y 701, which is determined by the length of theOFDM symbol, which the WiMAX standard 802.16e specifies as N=1024. Thus,typically, D<<L<<N.

Determining the coordinates b in equation (21) uses two paralleloperations. The first operation inverts T_(SS), which is simpler toperform than the N×N matrix inversions in equations (10) and (11). Thesecond operation projects the initial channel estimate h₁ 722 to a lowerdimension space, using an operation defined as,h_(S)=P_(S)h₁  (27)which is a D×1 vector. The operation of equation (27) is performed inthe initial estimate projection module 750, which generates output h_(S)752. The coordinates b are determined byb=−T _(SS) ⁻¹ h _(S)  (28)in the coordinates calculation module 770, from the inputs T_(SS) ⁻¹ 762and h_(S) 752.

The final operation is performed by the channel calculation module 780,which corrects the imperfections in the computation of h₁ to provide theimproved channel estimate g 782. This operation is simply,g=h ₁ +Gb  (29).Preferably, the hardware is selected through the arrangement and the useof MACs and signal paths so that the estimate g 782 is determined withinan OFDM symbol duration, that is, over N sample clock cycles.

FIG. 8 shows the operations for the stochastic LS-CE that preferably maybe used in an OFDM receiver (e.g., 220, 320 or 420) for appropriateenvironments such as when the second order statistics of the transmitsignal in the channel of interest are stable. The modifications relativeto the hardware in FIG. 7 are minimal, but can offer simplification andimplementation savings. The principal differences include that thedimension reduction module 840 accepts an L×L matrix R_(SS) 805 insteadof the convolutional matrix S 703 in FIG. 7.

As the inputs to the dimension reduction module 840 are different thanin its counterpart 740 in FIG. 7, the operations of module 840preferably are reconfigured. Specifically, equation (29) preferably isre-defined asP_(S)=G^(H)R_(SS)  (30)and equation (30) remains asT_(ss)=P_(S)G  (31)and these equations are implemented in the circuitry of dimensionreduction module 840. The simplification savings stem from assuming thatR_(SS) 805 is a constant matrix for all OFDM symbols input over time.

This assumption about the auto-covariance matrix R_(SS) is based on thefollowing observation. Depending on how the LS-CE is implemented for aparticular OFDM system, the design of the reference signal S (803 or703) may produce the condition that,{circumflex over (R)}_(SS)=S^(H)S≈R_(SS)  (32).The implication here is that the instantaneous auto-covariance matrix{circumflex over (R)}_(SS), which can be calculated at every symbol, maynot vary much from the long-term average. That is, R_(SS) is the averageof {circumflex over (R)}_(SS) over all time. Thus, for certain types ofOFDM symbols, regardless of the data present in the modulated carriers,the value of {circumflex over (R)}_(SS) does not vary significantly fromR_(SS).

The simplification achieved by implementing equation (30) rather thanequation (25) allows a hardware or software engineer to implement asimpler design according to aspects of the present invention. The LS-CEin FIG. 8 preferably also may be implemented as a lower-power version ofwhat is shown in FIG. 7.

The plot in FIG. 9 shows the improvement achieved by the LS-CE operationto improve the channel estimate from a simple cross-correlationcomputation as the initial estimate h₁ (722 or 822). In this example,the cycle prefix in the OFDM symbol is 128 samples, while the estimationexceeds that length. The length of 192 samples for estimation can leadto ill-conditioned R_(SS) matrices, as verified in simulations,resulting in an inability to directly perform the operation representedby equation (11). The estimate based on a simple cross-correlationbetween the local reference signal 803 and the input signal 801 is shownas h₁ 901. The application of the determined additive inverse, G_(D)b inequation (22), results in the much improved channel estimate 902, as inequation (22).

The inclusion of the LS-CE into a WiMAX simulator further demonstratedthe performance gains that can be obtained through implementation of theLS-CE. The WiMAX simulator used, Agilent Advanced Design System (ADS),performs better than implementable systems because the ADS knows somekey parameters to compute the system's frequency equalizer (FEQ) foreach received symbol. FIG. 10 shows the performance differences betweenthe ADS implementation and the modified receiver that computes the FEQcoefficients in the time domain with the LS-CE.

WiMAX allows for six different data rates to be transmitted on thedownlink, and FIG. 10 shows the performance for three of those datarates. At a 10⁻¹ link performance target, the LS-CE enabled receiver1012 offers about a 1 dB improvement over the ADS implementation 1011,when QPSK modulation is used on the data carriers. When the data rate isfurther increased by using 16 quadrature amplitude modulation (QAM), thegain is about 3.5 dB between the LS-CE enabled receiver 1022 and ADS1021. When switching to the most sensitive and highest throughput link,which uses 64 QAM, the LS-CE 1032 can establish a link to the user,while the ADS fails 1031.

Communication between a tower and a user may not achieve the bestpossible bit rate due to interference from adjacent towers and othersources. Therefore, interference cancellation, or at least some form ofmitigation, preferably is added to the receiver, since the simplest OFDMreceiver does not provide inherent interference mitigation, let alonecancellation, capabilities.

FIG. 11 shows the most basic OFDM receiver, which can also implement anadequate WiMAX receiver. The processing steps are conventional andinclude the OFDM receiver removing the cycle prefix (CP) 1110 from thereceived signal. Given the N pre-determined, and thus known to thereceiver, samples in an OFDM symbol, a single (serial) stream of samplesis reorganized into N parallel samples to feed fast Fourier transform(FFT) processor 1130. The next step is to obtain a frequency domainchannel estimate 1140 to properly equalize the signal to account for themultipath distortion in the channel. The coefficients, one per activecarrier in the OFDM symbol, are implemented with a frequency equalizer(FEQ) 1150. Subsequent to this equalization, the parallel stream ofsamples from the active data carriers is reconfigured as a serial stream1160 of samples for the demodulation processing 1170 which outputs thetransmitted bits.

The simple OFDM receiver in FIG. 11 can be designed to be cost effectiveand to achieve adequate receiver performance provided that the channeldistortions are confined to a restrictive set of conditions. If theseconditions are not met, such as if the channel coefficients exceed thecycle prefix (CP) length or excessive interference is present, then thefrequency domain channel estimator FDCE 1140 may lose accuracy as afunction of the severity of these distortions. This accuracy losspost-FFT processing is then manifested as an increase in bit error rateat the demodulator output 1170. Although equalizers are known to correctfor channel distortions, the OFDM receiver in FIG. 11 performs channelestimation after FFT processing and, consequently, the increasedcross-talk between carriers causes further signal degradation before thechannel is estimated.

Several aspects of the present invention are implemented in a preferredOFDM receiver, illustrated schematically in FIG. 12, which has a numberof advantages over the conventional FIG. 11 receiver. In the exampleillustrated in FIG. 12, channel estimation preferably is performed inthe time domain, thus offering a channel estimate that reduces theeffects of interference when compared to an equivalent estimation in thefrequency domain (1140 in FIG. 11). Most preferably, the FIG. 12receiver incorporates channel estimations as illustrated in either FIG.7 or FIG. 8 and described above, using a reference signal as illustratedin FIG. 6 and described above. FIG. 12 illustrates aspects of processingin a single antenna (SISO-type) OFDM receiver and more generally showstwo or more channels corresponding to a multiple base station ortransmitter OFDM system where the illustrated receiver detects signalsoutput by multiple transmitter antennas. Of course the receiversillustrated in the drawings are more generally parts of transceivers ormore complicated communications systems.

In any cell network deployment, signals from a plurality of basestations may reach a user with significant power. Preferredimplementations of the present invention readily provide forinterference mitigation, or cancellation, in OFDM systems by avoidingthe use of channel estimation in the frequency domain. The level ofinterference suppression for an OFDM communication system and hence, thescale of the complexity added to the generic receiver, is preferablyselected to achieve the target receiver operating characteristics in thepresence of expected multipath and interference. FIG. 12 illustrates thesimultaneous reception of signals from two base stations (1201 and 1202)but there may be signals received from a larger number of base stationsin practice. Typical cell-network design assigns different channels foreach corresponding station so that the signal from base station one 1201has a corresponding channel 1210. Likewise, the signal from base stationtwo 1202 has a corresponding channel 1220. A single antenna receiverreceives a sum 1250 of both channel outputs (1212 and 1222). In the caseof multiple antennas, there are a plurality of such additions andpreferably the multiple antenna receiver adopts appropriate channelestimation (e.g., estimation as shown in FIGS. 6-8 and discussed aboveand additions as shown in FIGS. 3-4 and discussed above) to correspondwith the underlying processes shown in FIG. 12.

To mitigate interference, preferred embodiments of the present inventionpreferably estimate each channel for each interferer. For the exampleshown in FIG. 12, one LC-CE unit 1230 determines the channel estimatefor one base station signal 1201 using an appropriate reference signal1231. Preferably, another LC-CE unit 1240 simultaneously determines thechannel estimate for the other base station signal 1202, also using theappropriate reference signal 1241. The estimation accuracy depends onthe orthogonality property between the two reference signals. Typically,as in WiMAX, the reference signals are designed to be orthogonal so thatthe correlation between the two reference signals is zero.

An interference mitigation module 1280 performs operations to mitigate asingle channel. Module 1280 offers the target suppression level for thebase station causing the interference, while maximizing the desired basestation's power. A plurality of approaches to such computations withvarying degrees of performance is known in the art. A preferredembodiment of the interference mitigation module 1280 performs a simpletransformation on the desired base station 1201 channel estimate 1232 toinclude a component of the interfering base station 1202 channelestimate 1242 for cancellation. A generalization of such a scheme relieson a linear mapping, performed through a matrix multiplication, betweenthe channel estimates 1232 and 1242 to a single channel estimate, whichis then transformed to the frequency domain by an appropriate FFToperation inside the module 1280. The module 1280 provides frequencydomain coefficients 1282 to the FEQ 1290.

Certain preferred embodiments preferably perform a linear transformationbetween the plurality of channel estimates to a single channel estimate,

$\begin{matrix}{c = {Ac}_{BS}} & (37) \\{{where},} & \; \\{c_{BS} = \begin{bmatrix}c_{1} \\c_{2}\end{bmatrix}} & (38)\end{matrix}$is the stacking of the channel estimates in the general case, and shownin equation (37) for two channel estimates. The matrix A is the linearcombination matrix which maps from the multiple channel estimates to asingle channel estimate c. An example of such a matrix may be,A=[1−g]  (39)where g is a complex value determined for each iteration of the channelestimation process 1230 and 1240. The variable g may be a magnitudescaling of for example,g_(max)=c₁ ^(H)c₂  (40).

A maximum interference mitigation is achieved when g=g_(max), but if thesimilarity between the channels is high, then the desired base stationpower may be insufficiently small following interference mitigation.Applying the linear transformation in equation (36), with g=g_(max),providesc ^(H) c ₁ =c ₁ ^(H) c ₁ −g _(max) c ₂ ^(H) c ₁ =c ₁ ^(H) c ₁ −|g_(max)|²  (41)and,c ^(H) c ₂ =c ₁ ^(H) c ₂ −g _(max) c ₂ ^(H) c ₂ =g _(max)(1−c ₂ ^(H) c₂)  (42).

The interference mitigation offered by equations (36)-(39) andimplemented in module 1280 offers a desirable level of performance forthe condition of “channel diversity.” This assumes that the similaritybetween the channels for each corresponding base station is not high. Ifchannel similarities are high, as in the case of flat rural areas, thenmore robust operations preferably are implemented in module 1280. Thedescribed process provides desirable performance advantages for manypractical implementations.

Any interference mitigation or cancellation scheme performance relies onthe channel estimation accuracy. The FIG. 12 implementation preferablyexploits channel diversity, even when the second base station's channelis not estimated at the receiver. For two channels, with |g_(max)|=0.62,FIG. 13 shows the improvement in packet-error rate in a WiMAX simulationat three power levels for the second base station. The implementationshown in FIG. 12, however, removes the calculations in 1240 and 1280 ofthe trivial case of g=0 given |g_(max)|=0.62. The performance gains arepresently believed to be associated with channel diversity and theaccuracy of the LS-CE 1230. The performance curves 1311, 1321 and 1331represent the performance with a preferred LS-CE 1230 in a WiMAXreceiver. The performance curves 1312, 1322 and 1332 represent a genericWiMAX receiver with some prior knowledge about the desired basestation's channel to calculate the channel estimate in the frequencydomain, similar to the receiver shown in FIG. 11.

The present invention has been described in terms of certain preferredembodiments. Those of ordinary skill in the art will appreciate thatvarious modifications and alterations could be made to the specificpreferred embodiments described here without varying from the teachingsof the present invention. Consequently, the present invention is notintended to be limited to the specific preferred embodiments describedhere but instead the present invention is to be defined by the appendedclaims.

I claim:
 1. A receiver for orthogonal frequency domain multiplexing(OFDM) signals, comprising: an initial channel estimator that generates,responsive to one or more pilot subchannels within a received OFDMsymbol comprising pilot and data subchannels, an initial time domainchannel impulse response estimate of a channel determined solely from atime period over which the received OFDM symbol was transmitted; a timedomain channel estimator coupled to receive the initial time domainchannel impulse response estimate, the time domain channel estimatorresponsive to the initial time domain channel impulse response estimateto generate a further time domain channel impulse response estimate thatmore accurately characterizes the time domain channel over which thereceived OFDM symbol was transmitted; and a frequency equalizerresponsive to the further time domain channel impulse response estimateto output an equalized signal responsive to the received OFDM symbol. 2.The receiver of claim 1, wherein the time domain channel estimator usesinformation about no more than one OFDM symbol to generate the furthertime domain channel impulse response estimate.
 3. The receiver of claim1, wherein the time domain channel estimator is further responsive to aplurality of pilot subchannels within the received OFDM symbol togenerate the further time domain channel impulse response estimate. 4.The receiver of claim 3, wherein the time domain channel estimatordetermines an autocovariance matrix of at least a portion of a transmitsignal and uses at least a portion of the autocovariance matrix togenerate the further time domain channel impulse response estimate. 5.The receiver of claim 4, wherein the time domain channel estimator usesinformation about only one OFDM symbol to generate the further timedomain channel impulse response estimate.
 6. The receiver of claim 1,further comprising an interference canceller receiving a time domainchannel impulse response estimate of an interference channel andcanceling at least a portion of an interfering signal portion of areceived input signal.
 7. The receiver of claim 1, wherein the timedomain channel estimator determines an autocovariance matrixcorresponding to at least a portion of a symbol and uses at least aportion of the autocovariance matrix to generate the further time domainchannel impulse response estimate.
 8. The receiver of claim 1, whereinthe initial channel estimator generates the initial time domain channelimpulse response estimate by cross-correlating a received time domainsignal with a time domain reference signal.
 9. The receiver of claim 8,wherein the time domain reference signal comprises generated pilotsignals and modulated zero value data signals.
 10. A receiver for anorthogonal frequency domain multiplexing (OFDM) system, the receivercomprising: an initial channel estimator responsive to a plurality ofpilots within a received OFDM symbol comprising pilots and data, theinitial channel estimator generating an initial time domain channelimpulse response estimate based on at least the plurality of pilotswithin the received OFDM symbol; a channel correction estimator thatgenerates a time domain channel impulse response correction to theinitial time domain channel impulse response estimate, the channelcorrection estimator responsive to the initial time domain channelimpulse response estimate to generate a set of basis vectors and togenerate the time domain channel impulse response correction as acombination of the set of basis vectors and a set of coordinates definedfor the set of basis vectors; a channel adder that adds the initial timedomain channel impulse response estimate with the time domain channelimpulse response correction and generates a further time domain channelimpulse response estimate; and a frequency equalizer responsive thefurther time domain channel impulse response estimate, the frequencyequalizer equalizing a signal derived from the received OFDM symbol. 11.The receiver of claim 10, wherein the channel correction estimator isresponsive to at least a portion of an autocorrelation matrix generatedfrom a vector including a plurality of pilots from the received OFDMsymbol as the channel correction estimator generates the time domainchannel impulse response correction.
 12. The receiver of claim 10,further comprising a reference signal generator that generates a timedomain reference signal comprising pilot signals and modulated zerovalue data signals.
 13. The receiver of claim 10, further comprising aninterference canceller receiving a time domain channel impulse responseestimate of an interference channel and canceling at least a portion ofan interfering signal portion of a received input signal.
 14. Thereceiver of claim 10, wherein the channel correction estimator receivesan autocorrelation matrix based on channel statistics and generates thetime domain channel impulse response correction in response to theinitial time domain channel impulse response estimate and theautocorrelation matrix.
 15. The receiver of claim 10, wherein thechannel correction estimator uses information about a single OFDM symbolto generate the further time domain channel impulse response estimate.16. The receiver of claim 10, wherein the channel correction estimatorgenerates a vector from the initial time domain channel impulse responseestimate to define a reduced dimension space, the channel correctionestimator using the vector in generating the further time domain channelimpulse response estimate.
 17. A receiver for an orthogonal frequencydomain multiplexing (OFDM) system, the receiver comprising: an initialchannel estimator that generates, responsive to a received OFDM symbol,an initial time domain channel impulse response estimate of a channeldetermined solely from a time period over which the received OFDM symbolwas transmitted; a channel correction estimator that receives theinitial time domain channel impulse response estimate and generates acurrent time domain channel impulse response correction to a currenttime domain channel impulse response estimate in response to at leastpilot subchannels within the received OFDM symbol; a channel estimatorthat adds a current time domain channel impulse response correction witha current time domain channel impulse response estimate and generates afurther time domain channel impulse response estimate in an iterativeprocess until a final time domain channel impulse response estimate isgenerated for the received OFDM symbol; and an equalizer that generatesa frequency equalizer based on the final time domain channel impulseresponse estimate, the equalizer module equalizing a signal derived fromthe received OFDM symbol.
 18. The receiver of claim 17, wherein thechannel correction estimator is responsive to at least a portion of anautocorrelation matrix generated from a vector including a plurality ofpilots as the channel correction estimator generates the current timedomain channel impulse response correction in response to the initialtime domain channel impulse response estimate.
 19. The receiver of claim18, wherein the initial channel estimator generates the initial timedomain channel impulse response estimate by cross-correlating a receivedtime domain signal with a time domain reference signal.
 20. The receiverof claim 19, wherein the time domain reference signal comprisesgenerated pilot signals and modulated zero value data signals.
 21. Thereceiver of claim 17, wherein the final time domain channel impulseresponse estimate is a minimum error channel estimate in a least squaressense.
 22. The receiver of claim 17, wherein the receiver usesinformation about a single OFDM symbol to generate the initial timedomain channel impulse response estimate and the final time domainchannel impulse response estimate.